Average Error: 0.2 → 0.0
Time: 7.7s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}
double f(double x) {
        double r1505539 = 6.0;
        double r1505540 = x;
        double r1505541 = 1.0;
        double r1505542 = r1505540 - r1505541;
        double r1505543 = r1505539 * r1505542;
        double r1505544 = r1505540 + r1505541;
        double r1505545 = 4.0;
        double r1505546 = sqrt(r1505540);
        double r1505547 = r1505545 * r1505546;
        double r1505548 = r1505544 + r1505547;
        double r1505549 = r1505543 / r1505548;
        return r1505549;
}
↓
double f(double x) {
        double r1505550 = 6.0;
        double r1505551 = x;
        double r1505552 = 1.0;
        double r1505553 = r1505551 + r1505552;
        double r1505554 = 4.0;
        double r1505555 = sqrt(r1505551);
        double r1505556 = r1505554 * r1505555;
        double r1505557 = r1505553 + r1505556;
        double r1505558 = r1505551 - r1505552;
        double r1505559 = r1505557 / r1505558;
        double r1505560 = r1505550 / r1505559;
        return r1505560;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.0
Herbie0.0
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

Derivation

  1. Initial program 0.2

    \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied associate-/l*0.0

    \[\leadsto \color{blue}{\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}}\]

  4. Final simplification0.0

    \[\leadsto \frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x)
  :name "Data.Approximate.Numerics:blog from approximate-0.2.2.1"
  :precision binary64

  :herbie-target
  (/ 6 (/ (+ (+ x 1) (* 4 (sqrt x))) (- x 1)))

  (/ (* 6 (- x 1)) (+ (+ x 1) (* 4 (sqrt x)))))